https://file.aiquickdraw.com/mathbot/file/1726261387382v0y2xjor.jpg

The expression in the image is:

\[
\frac{\sqrt{3}}{\sqrt{21}}
\]

To simplify this, we can combine the square roots under one square root as follows:

\[
\frac{\sqrt{3}}{\sqrt{21}} = \sqrt{\frac{3}{21}} = \sqrt{\frac{1}{7}}
\]

Therefore, the simplified form of the expression is:

\[
\frac{\sqrt{3}}{\sqrt{21}} = \frac{1}{\sqrt{7}}
\]

To rationalize the denominator, we multiply the numerator and denominator by \(\sqrt{7}\):

\[
\frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{7}}{7}
\]

So the final simplified expression is:

\[
\frac{\sqrt{7}}{7}
\]

Would you like any further explanation or details? 

Here are some related questions:
1. How do you rationalize a denominator?
2. What are the rules for simplifying square roots?
3. Can square roots always be simplified in terms of integers?
4. What is the importance of rationalizing the denominator?
5. How would the simplification change if there was an additional term?

**Tip:** Always try to simplify square roots and fractions first before rationalizing the denominator to make calculations easier.

Simplify the expression \( \frac{\sqrt{3}}{\sqrt{21}} \)

Learn how to simplify and rationalize the square root expression \( \frac{\sqrt{3}}{\sqrt{21}} \). The solution involves simplifying the square root and rationalizing the denominator, suitable for students in Grades 8-10.

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